On a low-friction track, a \(0.66-\mathrm{kg}\) cart initially going at \(1.85 \mathrm{~m} / \mathrm{s}\) to the right collides with a cart of unknown inertia initially going at \(2.17 \mathrm{~m} / \mathrm{s}\) to the left. After the collision, the \(0.66-\mathrm{kg}\) cart is going at \(1.32 \mathrm{~m} / \mathrm{s}\) to the left, and the cart of unknown inertia is going at \(3.22 \mathrm{~m} / \mathrm{s}\) to the right. The collision takes \(0.010 \mathrm{~s}\).

(a) What is the unknown inertia?

(b) What is the average acceleration of each cart?

(c) Use your answer to part \(a\) to check your answer to part \(b\).